UNIT 1: Sets, Relations and Functions
- Sets and their representation
- Union, intersection, and complement of sets
- Algebraic properties of sets
- Power set
- Relations: types and properties
- Functions: one-one, onto, and composition of functions
UNIT 2: Complex Numbers and Quadratic Equations
- Complex numbers as ordered pairs of reals
- Argand diagram representation
- Algebra of complex numbers
- Modulus and argument
- Quadratic equations in real and complex systems
- Relations between roots and coefficients
- Nature of roots and formation of equations
UNIT 3: Matrices and Determinants
- Definition and types of matrices
- Algebra of matrice
- Determinants (order 2 and 3)
- Properties of determinants
- Adjoint and inverse of a square matrix
- Area of triangle using determinants
- Consistency and solution of linear equations (2 or 3 variables)
UNIT 4: Permutations and Combinations
- Fundamental principle of counting
- Permutations (nPr)
- Combinations (nCr)
UNIT 5: Binomial Theorem
- Binomial theorem for positive integral index
- General term and middle term
- Simple applications
UNIT 6: Sequence and Series
- Arithmetic and Geometric progressions
- Insertion of means (A.M., G.M.)
- Relation between A.M. and G.M.
UNIT 7: Limit, Continuity and Differentiability
- Real-valued functions and types
- Algebra of functions
- Limits and continuity
- Differentiation: rules (sum, product, quotient, chain)
- Derivatives of polynomial, trigonometric, exponential, logarithmic, inverse trigonometric functions
- Implicit and parametric differentiation
- Second-order derivatives
- Applications:
- Rate of change
- Monotonicity
- Maxima and minima
UNIT 8: Integral Calculus
- Integration as anti-derivative
- Standard integrals (algebraic, trigonometric, exponential, logarithmic)
- Methods of integration: substitution, parts, partial fractions
- Integration using trigonometric identities
- Evaluation of simple and definite integrals
- Fundamental theorem of calculus
- Area under curves
UNIT 9: Differential Equations
- Order and degree of differential equations
- Formation of differential equations
- Solution by separation of variables
- Homogeneous equations
- Linear differential equations of type $\mathrm{\frac{dy}{dx} + P(x)y = Q(x)}$
UNIT 10: Coordinate Geometry
- Straight Line
- Equation of line in various forms
- Distance, section, and midpoint formulas
- Angle between two lines
- Condition for concurrence
- Intercepts on coordinate axes
- Circle
- Standard form and general equation of a circle
- Equation of tangent, chord, and pair of tangents
- Parabola
- Standard equation and parameters (vertex, focus, directrix)
- Tangent, normal, and focal properties
- Ellipse
- Standard equation and parameters (center, vertices, foci, eccentricity)
- Tangent and normal equations
- Auxiliary circle and related propertie
- Hyperbola
- Standard equation and parameters (center, foci, asymptotes, eccentricity)
- Tangent and normal equation
- Conjugate and transverse axes properties
UNIT 11: Three Dimensional Geometry
- Coordinates of a point in space
- Distance between two points
- Section formula
- Direction ratios and cosines
- Angle between two lines
- Equation of a line and plane
- Skew lines and shortest distance between them
UNIT 12: Vector Algebra
- Scalars and vectors
- Addition and subtraction of vectors
- Components of a vector in 2D and 3D
- Scalar (dot) product
- Vector (cross) product
- Applications in geometry
UNIT 13: Statistics and Probability
- Statistics
- Measures of dispersion: mean, median, mode
- Standard deviation, variance, mean deviation (grouped & ungrouped data)
- Probabilit
- Basic probability rule
- Addition and multiplication theorems
- Bayes’ theorem
- Probability distribution of random variables
UNIT 14: Trigonometry
- Trigonometric identities and equations
- Trigonometric functions and graphs
- Inverse trigonometric functions
- Properties and transformations
IIT JEE Main Maths Study Materials All Chapters
- Sets and Relations
- Functions
- Complex Numbers
- Quadratic Equations
- Matrices & Determinants
- Permutations & Combinations
- Binomial Theorem and Mathematical Induction
- Sequence & Series
- Limit, Continuity & Differentiability
- Differentiation
- Indefinite Integration
- definite integrals
- Area Under Curve
- Differential Equations
- Cartesian system of rectangular co-ordinates in a plane
- Straight Line
- Pair of Straight Line
- Circle
- Parabola
- Ellipse
- Hyperbola
- 3-Dimensional Geometry
- Vector Algebra
- Statistics
- Probability
- Trigonometrical identities and equations
- Trigonometrical functions.
- Inverse trigonometrical functions
- Mathematical Reasoning
Best books for JEE Main 2026 Maths
Mathematics is generally considered the toughest of all subjects and includes comprehensive problems on prescribed topics. Its preparation requires a lot of practice of relevant questions and deep understanding of concepts. Maths though is very scoring and if prepared well, you can score full marks, ultimately fetching you a good rank. The reference books for practising the problems of JEE Main mathematics are given here
Best books for JEE Main Maths
| S.No | Name of the book and author | Book will be best for |
|---|---|---|
| 1. | Objective Mathematics by R D Sharma | Basics of every topic |
| 2. | Plane Trigonometry by S L Loney | Trigonometry |
| 3. | The Elements Of Coordinate Geometry by S L Loney | Coordinate Geometry |
| 4. | Algebra by Dr S K Goyal Arihant Publications | Algebra |
| 5. | Play with Graphs by Amit M Agarwal (Arihant Publications) | For solving problems |
| 6. | Differential Calculus by Amit M Agarwal (Arihant Publications) | Calculus |
| 7. | Integral Calculus by Amit M Agarwal (Arihant Publications) | Calculus |
| 8. | Complete mathematics for JEE Main TMH | For explanation of topics |
JEE Main Maths Chapter Wise Weightage 2025
| Chapters | No. of Questions | Marks | Weightage (%) |
|---|---|---|---|
| Coordinate Geometry | 5 | 20 | 6.4% |
| Binomial Theorem and its Application | – | 4 | 3.2% |
| Differential Equation | – | 4 | 3.2% |
| Complex Numbers and Quadratic Equation | 2 | 8 | 6.4% |
| Limits, Continuity, and Differentiability | 3 | 12 | 10% |
| Differential Calculus | 1 | 4 | 3.2% |
| Matrices and Determinants | 2 | 8 | 6.4% |
| Integral Calculus | 3 | 12 | 10% |
| Statistics and Probability | 2 | 8 | 6.4% |
| Mathematical Reasoning | 1 | 4 | 3.2% |
| Sequences and Series | 1 | 4 | 3.2% |
| Permutations and Combinations | 1 | 4 | 3.2% |
| Three Dimensional Geometry | 2 | 8 | 6.4% |
| Sets, Relation, and Function | 1 | 4 | 3.2% |
| Trigonometry | 1 | 4 | 3.2% |
| Statics and Dynamics | 1 | 4 | 3.2% |
| Vector Algebra | 2 | 8 | 6.4% |
JEE Main 2026 Mathematics Syllabus
The Mathematics section of JEE Main 2026 will be of 100 marks (25 questions of 4 marks each). However, for any question answered incorrectly, one mark will be deducted. In 2015, the highest weightage in Mathematics was given to chapters like sequence and series, straight lines, 3D, Determinant, etc. Check out the detailed JEE Main January 2025 Paper 1 syllabus for Mathematics.
| Units | Topics |
|---|---|
| Unit 1: Sets, Relations and Functions | Sets and their representation; Union, intersection and complement of sets and their algebraic properties; Power set; Relations, type of relations, equivalence relations, functions; one-one, into and onto functions, the composition of functions. |
| Unit 2: Complex Numbers and Quadratic Equations | Complex numbers as ordered pairs of reals, Representation of complex numbers in the form \(a + ib\) and their representation in a plane, Argand diagram, algebra of complex numbers, modulus and argument (or amplitude) of a complex number, Quadratic equations in real and complex number systems and their solutions; Relations between roots and coefficients, nature of roots, the formation of quadratic equations with given roots. |
| Unit 3: Matrices and Determinants | Matrices, Algebra of matrices, type of matrices; Determinants and matrices of order two and three, evaluation of determinants, area of triangles using determinants; Adjoint, and evaluation of inverse of a square matrix using determinants; Test of consistency and solution of simultaneous linear equations in two or three variables using matrices. |
| Unit 4: Permutations and Combinations | The fundamental principle of counting, permutations and combinations; Meaning of \(P(n, r)\) and \(C(n, r)\). Simple applications. |
| Unit 5: Binomial Theorem and its Simple Applications | Binomial theorem for a positive integral index, General term and middle term and Simple applications. |
| Unit 6: Sequences and Series | Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers, Relation between A.M and G.M. |
| Unit 7: Limit, Continuity and Differentiability | Real–valued functions, algebra of functions; polynomial, rational, trigonometric, logarithmic and exponential functions; Inverse functions. Graphs of simple functions. Limits, continuity and differentiability. Differentiation of the sum, difference, product and quotient of two functions. Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, Composite and implicit functions; derivatives of order upto two, Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable. |
| Unit 8: Integral Calculus | Integral as an anti-derivative, Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions. Integration by substitution, by parts and by partial fractions. Integration using trigonometric identities. Evaluation of simple integrals of the type \( \int \frac{dx}{x^{2}+a^{2}},\quad \int \frac{dx}{\sqrt{x^{2}\pm a^{2}}},\quad \int \frac{dx}{a^{2}-x^{2}},\quad \int \frac{dx}{\sqrt{a^{2}-x^{2}}},\) \(\quad \int \frac{dx}{ax^{2}+bx+c},\quad \int \frac{dx}{\sqrt{ax^{2}+bx+c}},\quad \int \frac{(px+q)\,dx}{ax^{2}+bx+c},\quad \int \frac{(px+q)\,dx}{\sqrt{ax^{2}+bx+c}},\quad \int \sqrt{a^{2}\pm x^{2}}\,dx,\quad \int \sqrt{x^{2}-a^{2}}\,dx \) The fundamental theorem of calculus; Properties of definite integrals. Evaluation of definite integrals, Determining areas of the regions bounded by simple curves in standard forms. |
| Unit 9: Differential Equations | Ordinary differential equations, their order and degree, the solution of differential equation by the method of separation of variables, Solution of a homogeneous and linear differential equation of the type \[ \frac{dy}{dx} + p(x)\,y = q(x). \] |
| Unit 10: Co-ordinate Geometry | Cartesian system of rectangular coordinates in a plane, distance formula, sections formula, locus and its equation, the slope of a line, parallel and perpendicular lines, intercepts of a line on the co-ordinate axis. Straight line: Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, the distance of a point form a line, Co-ordinate of the centroid, orthocentre and circumcentre of a triangle. Circle, conic sections: A standard form of equations of a circle, the general form of the equation of a circle, its radius and centre, equation of a circle when the endpoints of a diameter are given, points of intersection of a line and a circle with the centre at the origin and sections of conics, Equations of conic sections (parabola, ellipse and hyperbola) in standard forms. |
| Unit 11: Three Dimensional Geometry | Coordinates of a point in space, the distance between two points, Section formula, direction ratios and direction cosines and the angle between two intersecting lines. Equation of a line; Skew lines, the shortest distance between them and its equation. |
| Unit 12: Vector Algebra | Vectors and scalars, the addition of vectors, components of a vector in two dimensions and three-dimensional spaces, scalar and vector products. |
| Unit 13: Statistics and Probability | Measures of dispersion; calculation of mean, median, mode of grouped and ungrouped data, calculation of standard deviation, variance and mean deviation for grouped and ungrouped data. Probability: Probability of an event, addition and multiplication theorems of probability, Baye’s theorem, probability distribution of a random variable. |
| Unit 14: Trigonometry | Trigonometrical identities and trigonometrical functions, inverse trigonometrical functions their properties. |